Statistics and Prob

Question

Twelve adults had their blood tested for sugar level (y, in mg/dL) given their corresponding ages (x)

x	25	30	35	40	42	45	48	49	50	52	53	55
y	95	80	99	99	80	100	104	120	125	100	120	125

The value of a in y=a+bx is ___________ ( in three decimal places)

Answer 1

Basically your question is asking for the y-intercept of the line of best fit.

In all of the classes I've had to use linear regression in, I've been permitted to use a calculator. So I will explain how I got my answer.

By Hand

y-hat= predicted y

x bar and y bar = mean of x and y values respectively

sx and sy= standard deviation of x and y respectively

n= number of data pairs

Stats Formulas

1. y-hat = b0 + b1x which is basically the same as y= a +bx
2. b1=r(sy/sx)
3. b0=y-bar -b1x
4. r=((x1-x bar)(y1-y bar) +(x2-x bar)(y2-ybar)+...+(xn-x bar)(yn-ybar))/((n-1)(sx)(sy))
5. sx=√((∑((x-xbar)^2))/(n-1))

.You need to know

1. mean of the x values= find the average by adding them all and dividing them by n.
2. n=12
3. x bar= 43.667
4. mean of the y values
5. n=12
6. y bar= 103.91666
7. standard deviation of x values
8. Follow the formula given above by adding (x1-x bar)^2 together. Like (25-43.667)^2+(30-...) and so on.
9. Then divide by n-1 which is 12-1= 11
10. After this, get the the square root. Your final answer should be 9.53780
11. standard deviation of y values
12. Repeat the same process
13. Your final answer should be 15.6928
14. correlation between X and Y
15. Multiply (x1-xbar) and (y1-ybar) and add to (x2-xbar)(y2-ybar) and so on to (x12-xbar)(y12-ybar)
16. divide this number sx, sy and 11
17. your answer should be .7074
18. now find b1, the slope,
19. multiply r=.7074 and sy= 15.6928= 11.10108672
20. Divide by sx= 9.53780
21. Your answer should be 1.16390
22. Now find b0 or a!
23. ybar=b0-b1xbar. This is just plugging in the mean values of x and y into the original formula
24. this means b0=ybar-b1x-bar
25. This is 103.916667- 1.16390(43.667)
26. =53.09299
27. =53.093

Graphing Calculator (I use a TI-84 Plus)

1. Clear your calculator (2nd, +, 7, 1, 2)
2. Hit Stat
3. Press 'Enter' or 1 to edit
4. Fill L1 or list one with all of the x values
5. Fill L2 or List two with all of the y values
6. Hit stat
7. Go right
8. Choose option 8 by either scrolling down and pressing enter or just typing 8.
9. Option 4 is Linear Regression for y=ax+b which can be confusing if you're in a rush and choose the wrong letter. However its okay if you did choose 4, just look at the first line and see what format the formula is in.
10. Make sure XList is L1 and Ylist is L2. If it isn't the right list, hit '2nd' and then 'stat' and then choose the right list. Hit enter.
11. Scroll down and hit enter on calculate
12. It will show you y=a+bx, then a's value and then b's. Copy down a. Which should be 53.0934... or 53.093 (since you definitely don't round up if the next digit is less than 5)

Hope this helps!